Differential Equations of Fractional Order: Methods, Results and Problems. II
Differential Equations of Fractional Order: Methods, Results and Problems. II
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DOI：
10.1080/0003681021000022032
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发表时间：
2002-01
影响因子：
1.1
通讯作者：
A. Kilbas;J. Trujillo
中科院分区：
文献类型：
--
作者：
A. Kilbas;J. Trujillo
这篇文章是第一篇文章的延续 [A.A.基尔巴斯和 J.J.特鲁希略（2001）。分数阶微分方程。方法、结果和问题，I. 应用分析，78 (1-2), 153-192.]，处理所谓的分数阶微分方程，其中在分数阶导数的运算下包含未知函数。介绍了此类分数阶微分方程理论中的方法和结果，包括普通分数阶微分方程的狄利克雷型问题，研究广义函数空间中的此类方程、部分分数阶微分方程和更一般的抽象方程，以及普通和部分分数阶微分方程数值方法的处理。讨论了研究中存在的问题和新趋势。
The article, being a continuation of the first one [A.A. Kilbas and J.J. Trujillo (2001). Differential equations of fractional order. Methods, results and problems, I. Applicable Analysis , 78 (1-2), 153-192.], deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. The methods and the results in the theory of such fractional differential equations are presented including the Dirichlet-type problem for ordinary fractional differential equations, studying such equations in spaces of generalized functions, partial fractional differential equations and more general abstract equations, and treatment of numerical methods for ordinary and partial fractional differential equations. Problems and new trends of research are discussed.